This paper concerns an epistemological objection against mathematical platonism, due to Hartry Field.The argument poses an explanatory challenge – the challenge to explain the reliability of our mathematical beliefs – which the platonist, it’s argued, cannot meet. Is the objection compelling? Philosophers disagree, but they also disagree on (and are sometimes very unclear about) how the objection should be understood. Here I distinguish some options, and highlight some gaps that need to be filled in on the potentially most compelling version (...) of the argument. (shrink)

This book is in honour of Professor Anna-Sofia Maurin on her 50th birthday. It consists of eighteen essays on metaphysical issues written by Swedish and international scholars.

The representation theorems of expected utility theory show that having certain types of preferences is both necessary and sufficient for being representable as having subjective probabilities. However, unless the expected utility framework is simply assumed, such preferences are also consistent with being representable as having degrees of belief that do not obey the laws of probability. This fact shows that being representable as having subjective probabilities is not necessarily the same as having subjective probabilities. Probabilism can be defended on the (...) basis of the representation theorems only if attributions of degrees of belief are understood either antirealistically or purely qualitatively, or if the representation theorems are supplemented by arguments based on other considerations (simplicity, consilience, and so on) that single out the representation of a person as having subjective probabilities as the only true representation of the mental state of any person whose preferences conform to the axioms of expected utility theory. (shrink)

I present a proof of the quantum probability rule from decision-theoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch's recent proof of the probability rule, but the proof is simpler and proceeds from weaker decision-theoretic assumptions. This makes it easier to discuss the conceptual ideas involved in the proof, and to show that they are defensible.

In this paper I examine a neglected question concerning the centerpiece of Carnap's philosophy: the principle of tolerance. The principle of tolerance states that we are free to devise and adopt any well-defined form of language or linguistic framework we please. A linguistic framework defines framework-internal standards of correct reasoning that guide us in our first-order scientific pursuits. The choice of a linguistic framework, on the other hand, is an ‘external’ question to be settled on pragmatic grounds and so not (...) itself constrained by these standards. However, even if choosing a framework is a practical matter, we would nevertheless expect the process of framework selection to be subject to rational norms. But which norms might those be? And where do they come from? I begin by showing that these questions are crucial to the success of Carnap's entire philosophical project. I then offer a response on behalf of the Carnapian which guarantees the rationality of the process of framework selection, while remaining true to Carnap's firm commitment to tolerance. (shrink)

(2013). Why humans are (sometimes) less rational than other animals: Cognitive complexity and the axioms of rational choice. Thinking & Reasoning: Vol. 19, No. 1, pp. 1-26. doi: 10.1080/13546783.2012.713178.

In this paper, a problem for utility theory - that it would have an agent who was compelled to play “Russian Roulette’ with one revolver or another, to pay as much to have a six-shooter with four bullets relieved of one bullet before playing with it, as he would be willing to pay to have a six-shooter with two bullets emptied - is reviewed. A less demanding Bayesian theory is described, that would have an agent maximize expected values of possible (...) total consequence of his actions. And utility theory is located within that theory as valid for agents who satisfy certain formal conditions, that is, for agents who are, in terms of that more general theory, indifferent to certain dimensions of ‘risk’. Raiffa- and Savage-style arguments for its more general validity are then resisted. Addenda are concerned with implications for game theory, and relations between ‘utilities’ and ‘values’. (shrink)

Two partition-theorems are proved for a particular causal decision theory. One is restricted to a certain kind of partition of circumstances, and analyzes the utility of an option in terms of its utilities in conjunction with circumstances in this partition. The other analyzes an option's utility in terms of its utilities conditional on circumstances and is quite unrestricted. While the first form seems more useful for applications, the second form may be of theoretical importance in foundational exercises. Comparisons are made (...) with theorems of Richard Jeffrey, Brad Armendt, and Peter Fishburn. (shrink)

Marx criticized political economy for propounding an inverted, mystical view of economic reality. But he went beyond asserting the falsity and apologetic character of the doctrine to characterize it as reflecting a social practice of inversion or mystification — an inverted social world — in which individuals incorporate their own actions into a process whose dynamic lies beyond their control. Caught up in this process, individuals confront aspects of their own agency in the alien or reified form of a given, (...) determining reality. Marx leaves unclear exactly how the process exerts and maintains its hold on agents, the nature of the reasons they might have for wanting to free themselves of it, and under what conditions they could do so. However, it is possible to abstract somewhat from Marx's specific concerns and to model a self-reproducing practice of reification that works through the informational environment of decision. Though of wider interest, this more general conception can shed light on the nature and critique of Marx's inverted world. It draws on conceptual resources from decision theory, game theory and general equilibrium theory. (shrink)

For Savage (1954) as for de Finetti (1974), the existence of subjective (personal) probability is a consequence of the normative theory of preference. (De Finetti achieves the reduction of belief to desire with his generalized Dutch-Book argument for Previsions.) Both Savage and de Finetti rebel against legislating countable additivity for subjective probability. They require merely that probability be finitely additive. Simultaneously, they insist that their theories of preference are weak, accommodating all but self-defeating desires. In this paper we dispute these (...) claims by showing that the following three cannot simultaneously hold: (i) Coherent belief is reducible to rational preference, i.e. the generalized Dutch-Book argument fixes standards of coherence. (ii) Finitely additive probability is coherent. (iii) Admissible preference structures may be free of consequences, i.e. they may lack prizes whose values are robust against all contingencies. (shrink)

The hypothesis that human reasoning and decision-making can be roughly modeled by Expected Utility Theory has been at the core of decision science. Accumulating evidence has led researchers to modify the hypothesis. One of the latest additions to the field is Dual Process theory, which attempts to explain variance between participants and tasks when it comes to deviations from Expected Utility Theory. It is argued that Dual Process theories at this point cannot replace previous theories, since they, among other things, (...) lack a firm conceptual framework, and have no means of producing independent evidence for their case. (shrink)

The two envelopes problem has generated a significant number of publications (I have benefitted from reading many of them, only some of which I cite; see the epilogue for a historical note). Part of my purpose here is to provide a review of previous results (with somewhat simpler demonstrations). In addition, I hope to clear up what I see as some misconceptions concerning the problem. Within a countably additive probability framework, the problem illustrates a breakdown of dominance with respect to (...) infinite partitions in circumstances of infinite expected utility. Within a probability framework that is only finitely additive, there are failures of dominance with respect to infinite partitions in circumstances of bounded utility with finitely many consequences (see the epilogue). (shrink)

The context-free weak ordering principle is viewed by many as a cornerstone of rational choice theory. McClennen, for example, claims that this principle is one of a pair on which '[t]he theory of rational choice and preference, as it has been developed in the past few decades by economists and decision theorists, rests', and Sen characterizes a version of context freedom as ‘a very basic requirement of rational choice’. But this principle is certainly not uncontroversial: there are examples of principle (...) is certainly not apper irrational. (shrink)

This paper presents an axiomatization of the principle of maximizing expected utility that does not rely on the independence axiom or sure-thing principle. Perhaps more importantly the new axiomatization is based on an ex ante approach, instead of the standard ex post approach. An ex post approach utilizes the decision maker's preferences among risky acts for generating a utility and a probability function, whereas in the ex ante approach a set of preferences among potential outcomes are on the input side (...) of the theory and the decision maker's preferences among risky acts on the output side. (shrink)

In Richard Bradley’s book, Decision Theory with a Human Face, we have selected two themes for discussion. The first is the Bolker-Jeffrey theory of decision, which the book uses throughout as a tool to reorganize the whole field of decision theory, and in particular to evaluate the extent to which expected utility theories may be normatively too demanding. The second theme is the redefinition strategy that can be used to defend EU theories against the Allais and Ellsberg paradoxes, a strategy (...) that the book by and large endorses, and even develops in an original way concerning the Ellsberg paradox. We argue that the BJ theory is too specific to fulfil Bradley’s foundational project and that the redefinition strategy fails in both the Allais and Ellsberg cases. Although we share Bradley’s conclusion that EU theories do not state universal rationality requirements, we reach it not by a comparison with BJ theory, but by a comparison with the non-EU theories that the paradoxes have heuristically suggested. (shrink)

It is argued that existing axiomatic theories of utility do not provide the utility principle or the principle of maximising expected utility with a formal justification. It is also argued that these theories only put mild constraints on a decision-maker in a decision-context. Finally, it is argued that the prospects are not particularly bright for finding formal non-circular arguments for the utility principle that do not rely on the law of large numbers.

This paper places formal learning theory in a broader philosophical context and provides a glimpse of what the philosophy of induction looks like from a learning-theoretic point of view. Formal learning theory is compared with other standard approaches to the philosophy of induction. Thereafter, we present some results and examples indicating its unique character and philosophical interest, with special attention to its unified perspective on inductive uncertainty and uncomputability.

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

In his Truth and Probability (1926), Frank Ramsey provides foundations for measures of degrees of belief in propositions and preferences for worlds. Nonquantitative conditions on preferences for worlds, and gambles for worlds and certain near-worlds, are formulated which he says insure that a subject's preferences for worlds are represented by numbers, world values. Numbers, for his degrees of belief in propositions, probabilities, are then defined in terms of his world values. Ramsey does not also propose definitions of desirabilities for propositions, (...) though he is in a position to do this. Given his measures for probabilities of propositions and values of worlds, he can frame natural definitions for both evidential and causal desirabilities that would measure respectively the welcomeness of propositions as items of news, and as facts. His theory is neutral with respect to the evidential/causal division. In the present paper, as Ramsey's foundations are explained, several problems and limitations are noted. Their distinctive virtue – their evidential/causal neutrality – is demonstrated. Comparisons are made with other foundational schemes, and a perspective is recommended from which nonquantitative foundations are not the be all for quantitative theories of ideal preferences and credences. (shrink)

We discuss the meaning of probabilities in the many worlds interpretation of quantum mechanics. We start by presenting very briefly the many worlds theory, how the problem of probability arises, and some unsuccessful attempts to solve it in the past. Then we criticize a recent attempt by Deutsch to derive the quantum mechanical probabilities from the nonprobabilistic parts of quantum mechanics and classical decision theory. We further argue that the Born probability does not make sense even as an additional probability (...) rule in the many worlds theory. Our conclusion is that the many worlds theory fails to account for the probabilistic statements of standard (collapse) quantum mechanics. (shrink)

Difficulties over probability have often been considered fatal to the Everett interpretation of quantum mechanics. Here I argue that the Everettian can have everything she needs from `probability' without recourse to indeterminism, ignorance, primitive identity over time or subjective uncertainty: all she needs is a particular *rationality principle*. The decision-theoretic approach recently developed by Deutsch and Wallace claims to provide just such a principle. But, according to Wallace, decision theory is itself applicable only if the correct attitude to a future (...) Everettian measurement outcome is subjective uncertainty. I argue that subjective uncertainty is not to be had, but I offer an alternative interpretation that enables the Everettian to live without uncertainty: we can justify Everettian decision theory on the basis that an Everettian should *care about* all her future branches. The probabilities appearing in the decision-theoretic representation theorem can then be interpreted as the degrees to which the rational agent cares about each future branch. This reinterpretation, however, reduces the intuitive plausibility of one of the Deutsch -Wallace axioms. (shrink)

In the debate between simple inference heuristics and complex decision mechanisms, we take a position squarely in the middle. A decision making process that extends to both naturalistic and novel settings should extend beyond the confines of this debate; both simple heuristics and complex mechanisms are cognitive skills adapted to and appropriate for some circumstances but not for others. Rather than ask `Which skill is better?'' it is often more important to ask `When is a skill justified?'' The selection and (...) application of an appropriate cognitive skill for a particular problem has both costs and benefits, and therefore requires the resolution of a tradeoff. In revisiting satisficing, we observe that the essence of satisficing is tradeoff. Unlike heuristics, which derive their justification from empirical phenomena, and unlike optimal solutions, which derive their justification by an evaluation of alternatives, satisficing decision-making derives its justification by an evaluation of consequences. We formulate and present a satisficing decision paradigm that has its motivation in Herbert Simon''s work on bounded rationality. We characterize satisficing using a cost–benefit tradeoff, and generate a decision rule applicable to both designing intelligent machines as well as describing human behavior. (shrink)

A generalization of the usual approach to the expected utility theory is given, with the aim of representing the state of belief of an agent who may decline on grounds of ignorance to express a preference between a given pair of acts and would, therefore, be considered irrational from a Bayesian point of view. Taking state, act, and outcome as primitive concepts, a utility function on the outcomes is constructed in the usual way. Each act is represented by a utility-valued (...) function on the states — but not all such functions are taken to represent acts. A weaker than usual set of axioms on preferences between acts is now postulated. It is shown that any agent can be represented by a risk function that assigns to each (mixed) state a number that gives the maximum loss (in utility) the agent might expect should be the actual state of the world. The form of the risk function is determined, both in general and in important particular cases. The results show that any rational agent behaves as though he were acting under the guidance of a set of Bayesian (or, more generally, pseudo-Bayesian) advisors. (shrink)

In his classic book “the Foundations of Statistics” Savage developed a formal system of rational decision making. The system is based on (i) a set of possible states of the world, (ii) a set of consequences, (iii) a set of acts, which are functions from states to consequences, and (iv) a preference relation over the acts, which represents the preferences of an idealized rational agent. The goal and the culmination of the enterprise is a representation theorem: Any preference relation that (...) satisfies certain arguably acceptable postulates determines a (finitely additive) probability distribution over the states and a utility assignment to the consequences, such that the preferences among acts are determined by their expected utilities. Additional problematic assumptions are however required in Savage's proofs. First, there is a Boolean algebra of events (sets of states) which determines the richness of the set of acts. The probabilities are assigned to members of this algebra. Savage's proof requires that this be a σ-algebra (i.e., closed under infinite countable unions and intersections), which makes for an extremely rich preference relation. On Savage's view we should not require subjective probabilities to be σ-additive. He therefore finds the insistence on a σ-algebra peculiar and is unhappy with it. But he sees no way of avoiding it. Second, the assignment of utilities requires the constant act assumption: for every consequence there is a constant act, which produces that consequence in every state. This assumption is known to be highly counterintuitive. The present work contains two mathematical results. The first, and the more difficult one, shows that the σ-algebra assumption can be dropped. The second states that, as long as utilities are assigned to finite gambles only, the constant act assumption can be replaced by the more plausible and much weaker assumption that there are at least two non-equivalent constant acts. The second result also employs a novel way of deriving utilities in Savage-style systems -- without appealing to von Neumann-Morgenstern lotteries. The paper discusses the notion of “idealized agent" that underlies Savage's approach, and argues that the simplified system, which is adequate for all the actual purposes for which the system is designed, involves a more realistic notion of an idealized agent. (shrink)

In this article, I examine the consequences of Mamou’s recent solution to the so-called problem of reindividuation. The problem is first proposed by John Broome as an argument against the Humean view of rationality and subjective decision theory. Essentially, Broome argues that the reindividuation of outcomes must be constrained in some way if the axioms of rationality are not to be vacuous, but the constraints on individuation cannot be consistent with the Humean view of rationality. Mamou offers an elegant Humean (...) solution to this problem. We do not need such rules for reindividuation since the subjective decision theory operates under the assumption of maximal relevance of description, and only under that assumption do the axioms tell anything. Thus the problem of reindividuation dissolves in a quite natural and simple way. However, I argue that if we connect this solution to the topic of justification for the requirements of rationality, problems arise. I examine the influence of the solution on the common argument for the axioms of decision theory, the so-called money-pump arguments. These arguments are a staple in the justification of the axioms of subjective decision theory. I argue that they are in collision with Mamou’s solution. This collision brings us to the dilemma: either accept Broome’s conclusions or lose the money-pump arguments as an effective tool for justification of the axioms. I conclude that neither of the options is really good for the defenders of the Humean view of rationality. (shrink)

The standard representation theorem for expected utility theory tells us that if a subject’s preferences conform to certain axioms, then she can be represented as maximising her expected utility given a particular set of credences and utilities—and, moreover, that having those credences and utilities is the only way that she could be maximising her expected utility. However, the kinds of agents these theorems seem apt to tell us anything about are highly idealised, being always probabilistically coherent with infinitely precise degrees (...) of belief and full knowledge of all a priori truths. Ordinary subjects do not look very rational when compared to the kinds of agents usually talked about in decision theory. In this paper, I will develop an expected utility representation theorem aimed at the representation of those who are neither probabilistically coherent, logically omniscient, nor expected utility maximisers across the board—that is, agents who are frequently irrational. The agents in question may be deductively fallible, have incoherent credences, limited representational capacities, and fail to maximise expected utility for all but a limited class of gambles. (shrink)

This research examined whether youth's forecasted risk taking is best predicted by a compensatory (namely, subjective expected utility) or non-compensatory (e.g., single-factor) model. Ninety youth assessed the importance of perceived benefits, importance of perceived drawbacks, subjective probability of benefits, and subjective probability of drawbacks for 16 risky behaviors clustered evenly into recreational and health/safety domains. In both domains, there was strong support for a noncompensatory model in which only the perceived importance of the benefits of engaging in a risky behavior (...) predicted youths' forecasted engagement in risky behavior. The study overcomes earlier methodological weaknesses by fully decomposing participants' assessments into importance and probability aspects for both benefits and drawbacks. As such, the findings provide clear evidence in support of a boundedrationality perspective on youth decision making regarding risk taking. (shrink)

A fundamental philosophical question that arises in connection with evolutionary theory is whether the fittest patterns of behavior are always the most rational. Are fitness and rationality fully compatible? When behavioral rationality is characterized formally as in classical decision theory, the question becomes mathematically meaningful and can be explored systematically by investigating whether the optimally fit behavior predicted by evolutionary process models is decision-theoretically coherent. Upon investigation, it appears that in nontrivial evolutionary models the expected behavior is not always in (...) accord with the norms of the standard theory of decision as ordinarily applied. Many classically irrational acts, e.g. betting on the occurrence of one event in the knowledge that the probabilities favor another, can under certain circumstances constitute adaptive behavior.One interesting interpretation of this clash is that the criterion of rationality offered by classical decision theory is simply incorrect (or at least incomplete) as it stands, and that evolutionary theory should be called upon to provide a more generally applicable theory of rationality. Such a program, should it prove feasible, would amount to the logical reduction of the theory of rational choice to evolutionary theory. (shrink)

The orthodox theory of instrumental rationality, expected utility (EU) theory, severely restricts the way in which risk-considerations can figure into a rational individual's preferences. It is argued here that this is because EU theory neglects an important component of instrumental rationality. This paper presents a more general theory of decision-making, risk-weighted expected utility (REU) theory, of which expected utility maximization is a special case. According to REU theory, the weight that each outcome gets in decision-making is not the subjective probability (...) of that outcome; rather, the weight each outcome gets depends on both its subjective probability and its position in the gamble. Furthermore, the individual's utility function, her subjective probability function, and a function that measures her attitude towards risk can be separately derived from her preferences via a Representation Theorem. This theorem illuminates the role that each of these entities plays in preferences, and shows how REU theory explicates the components of instrumental rationality. (shrink)

This paper reconstructs and evaluates the representation theorem presented by Ramsey in his essay 'Truth and Probability', showing how its proof depends on a novel application of Hölder's theory of measurement. I argue that it must be understood as a solution to the problem of measuring partial belief, a solution that in many ways remains unsurpassed. Finally I show that the method it employs may be interpreted in such a way as to avoid a well known objection to it due (...) to Richard Jeffrey. (shrink)

This paper reconstructs and evaluates the representation theorem presented by Ramsey in his essay 'Truth and Probability', showing how its proof depends on a novel application of Hölder's theory of measurement. I argue that it must be understood as a solution to the problem of measuring partial belief, a solution that in many ways remains unsurpassed. Finally I show that the method it employs may be interpreted in such a way as to avoid a well known objection to it due (...) to Richard Jeffrey. (shrink)

This paper provides new foundations for Bayesian Decision Theory based on a representation theorem for preferences defined on a set of prospects containing both factual and conditional possibilities. This use of a rich set of prospects not only provides a framework within which the main theoretical claims of Savage, Ramsey, Jeffrey and others can be stated and compared, but also allows for the postulation of an extended Bayesian model of rational belief and desire from which they can be derived as (...) special cases. The main theorem of the paper establishes the existence of a such a Bayesian representation of preferences over conditional prospects, i.e. the existence of a pair of real-valued functions respectively measuring the agent’s degrees of belief and desire and which satisfy the postulated rationality conditions on partial belief and desire. The representation of partial belief is shown to be unique and that of partial desire, unique up to a linear transformation. (shrink)

ABSTRACTThis paper addresses the problem of opaque sweetening and argues that one should use stochastic dominance in comparing lotteries even when dealing with incomplete orderings that allow for non-comparable outcomes.

Frank Plumpton Ramsey (1903–30) made seminal contributions to philosophy, mathematics and economics. Whilst he was acknowledged as a genius by his contemporaries, some of his most important ideas were not appreciated until decades later; now better appreciated, they continue to bear an influence upon contemporary philosophy. His historic significance was to usher in a new phase of analytic philosophy, which initially built upon the logical atomist doctrines of Bertrand Russell and Ludwig Wittgenstein, raising their ideas to a new level of (...) sophistication, but ultimately he became their successor rather than remain a mere acolyte. (shrink)

My dissertation explores the ways in which Rudolf Carnap sought to make philosophy scientific by further developing recent interpretive efforts to explain Carnap’s mature philosophical work as a form of engineering. It does this by looking in detail at his philosophical practice in his most sustained mature project, his work on pure and applied inductive logic. I, first, specify the sort of engineering Carnap is engaged in as involving an engineering design problem and then draw out the complications of design (...) problems from current work in history of engineering and technology studies. I then model Carnap’s practice based on those lessons and uncover ways in which Carnap’s technical work in inductive logic takes some of these lessons on board. This shows ways in which Carnap’s philosophical project subtly changes right through his late work on induction, providing an important corrective to interpretations that ignore the work on inductive logic. Specifically, I show that paying attention to the historical details of Carnap’s attempt to apply his work in inductive logic to decision theory and theoretical statistics in the 1950s and 1960s helps us understand how Carnap develops and rearticulates the philosophical point of the practical/theoretical distinction in his late work, offering thus a new interpretation of Carnap’s technical work within the broader context of philosophy of science and analytical philosophy in general. (shrink)

An extended analysis is given of the program, originally suggested by Deutsch, of solving the probability problem in the Everett interpretation by means of decision theory. Deutsch's own proof is discussed, and alternatives are presented which are based upon different decision theories and upon Gleason's Theorem. It is argued that decision theory gives Everettians most or all of what they need from `probability'. Contact is made with Lewis's Principal Principle linking subjective credence with objective chance: an Everettian Principal Principle is (...) formulated, and shown to be at least as defensible as the usual Principle. Some consequences of (Everettian) quantum mechanics for decision theory itself are also discussed. -/- [NB: this this long (70 pages) and occasionally rambling online-only paper has been almost entirely superseded by material in subsequent; if something is not included in them it usually means that I have had second thoughts. I include it for completeness only. (shrink)

This paper begins with a puzzle regarding Lewis' theory of radical interpretation. On the one hand, Lewis convincingly argued that the facts about an agent's sensory evidence and choices will always underdetermine the facts about her beliefs and desires. On the other hand, we have several representation theorems—such as those of (Ramsey 1931) and (Savage 1954)—that are widely taken to show that if an agent's choices satisfy certain constraints, then those choices can suffice to determine her beliefs and desires. In (...) this paper, I will argue that Lewis' conclusion is correct: choices radically underdetermine beliefs and desires, and representation theorems provide us with no good reasons to think otherwise. Any tension with those theorems is merely apparent, and relates ultimately to the difference between how 'choices' are understood within Lewis' theory and the problematic way that they're represented in the context of the representation theorems. For the purposes of radical interpretation, representation theorems like Ramsey's and Savage's just aren't very relevant after all. (shrink)

Taking Savage's subjective expected utility theory as a starting point, this thesis distinguishes three types of uncertainty which are incompatible with Savage's theory for small worlds: ambiguity, option uncertainty and state space uncertainty. Under ambiguity agents cannot form a unique and additive probability function over the state space. Option uncertainty exists when agents cannot assign unique consequences to every state. Finally, state space uncertainty arises when the state space the agent constructs is not exhaustive, such that unforeseen contingencies can occur. (...) Chapter 2 explains Savage's notions of small and large worlds, and shows that ambiguity, option and state space uncertainty are incompatible with the small world representation. The chapter examines whether it is possible to reduce these types of uncertainty to one another. Chapter 3 suggests a definition of objective ambiguity by extending Savage's framework to include an exogenous likelihood ranking over events. The definition allows for a precise distinction between ambiguity and ambiguity attitude. The chapter argues that under objective ambiguity, ambiguity aversion is normatively permissible. Chapter 4 gives a model of option uncertainty. Using the two weak assumptions that the status quo is not uncertain, and that agents are option uncertainty averse, we derive status quo bias, the empirical tendency for agents to choose the status quo over other available alternatives. The model can be seen as rationalising status quo bias. Chapter 5 gives an axiomatic characterisation and corresponding representation theorem for the priority heuristic, a heuristic which predicts binary decisions be- tween lotteries particularly well. The chapter analyses the normative implications of this descriptive model. Chapter 6 defends the pluralist view of decision theory this thesis assumes. The chapter discusses possible applications of the types of uncertainty defined in the thesis, and concludes. (shrink)

Savage's framework of subjective preference among acts provides a paradigmatic derivation of rational subjective probabilities within a more general theory of rational decisions. The system is based on a set of possible states of the world, and on acts, which are functions that assign to each state a consequence€. The representation theorem states that the given preference between acts is determined by their expected utilities, based on uniquely determined probabilities (assigned to sets of states), and numeric utilities assigned to consequences. (...) Savage's derivation, however, is based on a highly problematic well-known assumption not included among his postulates: for any consequence of an act in some state, there is a "constant act" which has that consequence in all states. This ability to transfer consequences from state to state is, in many cases, miraculous -- including simple scenarios suggested by Savage as natural cases for applying his theory. We propose a simplification of the system, which yields the representation theorem without the constant act assumption. We need only postulates P1-P6. This is done at the cost of reducing the set of acts included in the setup. The reduction excludes certain theoretical infinitary scenarios, but includes the scenarios that should be handled by a system that models human decisions. (shrink)